Abstract
In the paper problems with a dynamic decoupling of multi-input multi-output MIMO fractional order systems are discussed. Similarities and differences to integer order decoupling methods are shown. Basing on a few examples taken from a literature simulations of decoupled fractional order systems were caried out. Te paper ends with some final remarks on a practical implementation of decoupling methods for fractional order systems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Adolfsson, K., Enelund, I., Olsson, P.: On the fractional order model of viscoelasticity. Mech. Time-Depend. Mater. 9, 15–34 (2005)
Bristol, E.H.: On a new measure of interaction for multivariable process control. IEEE Trans. Autom. Control. AC–11, 133–134 (1966)
Chen, YQ., Petras, I., Xue, D.: Fractional order control—a tutorial. In: Proceedings of the American Control Conference, pp. 1397–1411. St. Louis (2009)
CRONE Toolbox. www.ims-bordeaux.fr/CRONE/toolbox/ (2014)
Domek, S.: Rachunek różniczkowy ułamkowego rzedu w regulacji predykcyjnej. Wydawnictwo Uczelniane ZUT, Szczecin (2013)
Dworak, P., Bańka, S.: Efficient algorithm for synthesis of multipurpose control systems with dynamic decoupling. MMAR05, pp. 345–350. Miedzyzdroje (2005)
Dworak, P.: Squaring down plant model and I/O grouping strategies for a dynamic decoupling of left-invertible MIMO plants. Bull. Pol. Acad. Sci. Tech. Sci. 62(3), 471–479 Sept 2014. ISSN (Online): 2300-1917, doi:10.2478/bpasts-2014-0050
Dworak, P.: Dynamic decoupling of left-invertible MIMO LTI plants. Arch. Control. Sci. 21(4), 443–459 (2011)
Dzieliński, A., Sierociuk, D.: Ultracapacitor modelling and control using discrete fractional order state-space model. Acta Montan. Slovaca 13(1), 136–145 (2008)
Garrido, J., Vazquez, F. Morilla, F.: Generalized inverted decoupling for TITO processes. In: Proceedings of the18th IFAC World Congress, pp. 7535–7540. Milano, Italy (2011)
Ghosh, A., Das, S.K.: Open-loop decoupling of MIMO plants. IEEE Trans. Autom. Control. 54(8), 1977–1981 (2009)
Jesus, I.S., Machado, J.T.: Application of integer and fractional models in electrochemical. Math. Probl. Eng. 2012, 248175 (2012)
Kaczorek, T.: Selected problems of fractional systems theory. Springer, Berlin (2011)
Latawiec, J.K., Lukaniszyn, M., Stanisławski, R.: Advances in modelling and control of non-integer order systems. Springer, New York (2014)
Li, Y., Chen, YQ.: Fractional order universal adaptive stabilization for fractional order MIMO system. In: Proceedings of the 4th IFAC Workshop Fractional Differentiation and its Applications, Badajoz, Spain (2010)
Li, Z., Chen, YQ.: Ideal, simplified and inverted decoupling of fractional order TITO processes. In: Proceedings of the 19th World Congress The International Federation of Automatic Control, pp. 2897–2902. Cape Town, South Africa (2014)
Li, Z., Chen, YQ.: Identificationof linear fractional order systems using the relay feedback approach. In: Proceedings of the American Control Conference, Portland, OR, USA (2014)
Liao, Z., Peng, C., Wang, Y.: A frequency-domain identification algorithm for MIMO fractional order systems with time-delay in state. Adv. Mater. Res. 383–390, 4397–4404 (2012)
Machado, J.T.: Fractional control of heat diffusion systems. Nonlinear Dyn. 54(3), 263–282 (2012)
Migan, R.: Fractional calculus in bioengineering. Begell House, Redding (2006)
Mitkowski, W., Kacprzyk, J., Baranowski, J.: Avances in the theory and applications of non-integer order systems. Springer, New York (2013)
Monje, C.A., Chen, Y.Q., Vinagre, J.B. M., Xue, D. Y., Feliu, V.: Fractional order systems and controls: fundamentals and applications. Springer, London (2010)
Oldham, K.B., Spanier, J.: The fractional calculus; theory and application of differentiation and integration to arbitrary order. Academic Press, New York (1974)
Oustaloup, A., Sabatier, J., Moreau, X.: From fractal robustness to CRONE approach. ESAIM 5, 177–192 (1998)
Oustaloup, A., Levron, F., Mathieu, B., Nanot, F.M.: Frequency-band complex noninteger differentiator: characterisation and synthesis. IEEE Trans. Circut Syst. 47(1), 25–39 (2000)
Petras, I.: Fractional-order nonlinear systems: modeling, analysis and simulation. Springer, New York (2011)
Podlubny, I.: Fractional differential equations. Academic Press, San Diego (1999)
Sabatier, J., Aoun, M., Oustaloup, A., Gregoire, G., Ragot, F., Roy, P.: Fractional system identification for lead acid battery state of charge estimation. Signal Process. 86(10), 2645–2650 (2006)
Sierociuk, D.: Estymacja i sterowanie dyskretnych układów dynamicznych ułamkowego rzedu opisanych w przestrzeni stanu. Politechnika Warszawska (2007)
Sierociuk, D., Macias, M., Malesza, W.: Analog modeling of fractional switched order derivative using different switching schemes. IEEE J. Emerg. Sel. Top. Circuts Syst. 3(3), 394–403 (2013)
Skovranek, T., Podlubny, I., Petras, I.: Modeling of the national economies in state-space: a fractional approach. Econ. Model. 29(4), 1322–1327 (2012)
Tavazoei, M.S., Tavakoli-Kakhki, M.: Minimal realizations for some classes of fractional order transfer functions. IEEE J. Emerg. Sel. Top. Circuts Syst. 3(3) (2013)
Toolbox ninteger for Matlab. http://web.ist.utl.pt/duarte.valerio/ninteger/ninteger.htm (2014)
Valerio, D., Costa, J.: Ninteger: a non-integer control toolbox for Matlab. In: Proceedings of the 1st IFAC Workshop on Fractional Differentiation and its Applications, pp. 208–213. Bordeaux, France (2004)
Williams, T.W.C., Antsaklis, P.J.: A unifying approach to the decoupling of linear multivariable systems. Int. J. Control. 44(1), 181–201 (1986) Tech. Sci. 62(3), 471–479 (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Dworak, P. (2016). On Dynamic Decoupling of MIMO Fractional Order Systems. In: Domek, S., Dworak, P. (eds) Theoretical Developments and Applications of Non-Integer Order Systems. Lecture Notes in Electrical Engineering, vol 357. Springer, Cham. https://doi.org/10.1007/978-3-319-23039-9_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-23039-9_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23038-2
Online ISBN: 978-3-319-23039-9
eBook Packages: EngineeringEngineering (R0)